I had explained in one of my earlier posts the concept of significant deficiency. A material weakness on the other hand is defined as:

" A Significant Deficiency in an internal control component that by itself or in aggregate that precludes the entity's internal control from reducing to an appropriately low level the risk that material mis-statements in financial statements will not be prevented or detected on a timely basis".

The main difference between a material weakness and a significant deficiency is that a material weakness in internal control is already a significant deficiency. However, a significant deficiency is not neccesarliy a material weakness.

More on Internal Controls >>

Corporate Code of Ethics , Designing Internal Controls in Four Easy Steps , Preventive Vs. Detective Controls